I have a very clear picture of the aesthetic of German fascism from the likes of Leni Riefenstahl, but what did fascism look like in other countries? Was there such a well developed aesthetic to Japanese or Italian fascism?

This question is a bit old at this point, but it overlaps really well with the topic of my thesis so I will take a shot at answering it. I can only speak on Italian Fascism, as that's what my research has focused on.

While Italian Fascism employed a number of different architectural styles, the most prominent style used for propaganda purposes was a sort of neo-classical architecture. As you may have heard, Mussolini frequently attempted to portray himself as some sort of Roman Emperor (especially through the legacy of Augustus Caesar), and to make Fascism seem like a movement which would restore the glories of Ancient Rome. Mussolini employed a number of means to further this message, but architecture was among the most prominent for a variety of reasons.

There are a couple great examples to demonstrate this. For one, take a look at the Foro Mussolini, now known as the Foro Italico. This was originally supposed to host the Olympics, and was therefore built with an international audience in mind - just like Hitler would do in 1936, Mussolini intended to use the Olympics as a propaganda showpiece. Ultimately, Italy was not chosen to host the Olympics for that cycle, and the games were eventually cancelled due to the outbreak of WWII, but the forum remains nonetheless. Within the Foro Italico, you'll find plentiful use of Greco-Roman figures and architectural styles, with references to Mussolini and Fascism interspersed among mosaics depicting ancient athletes. As such, Fascism is made to appear as having a deep kinship with the ancient world. Latin, the language of ancient Rome, was also used to further this message - the Foro includes a large obelisk which is dedicated to "MVSSOLINI DVX", Latin for "Mussolini the Leader."

Another great case study is the Via dell'Impero, or "Road of the Empire" (today known as the Via dei Fori Imperiali, or "road of the emperor's forum"). Constructed by the Fascist government, this road was designed to frame Mussolini's speeches which were typically delivered from a nearby palace. The road allowed Mussolini to address crowds in the shadow of the ancient Coliseum, framing his oratory with the imposing legacy of the Romans.

These first two examples are emblematic of the attempts by Mussolini's government to frame their regime with the legacy of the Romans - a goal which was pursued through many means, including architecture, as your question specifies. However, this isn't really a comprehensive picture of architecture in Fascist Italy. While neo-classical styles were prominent, the Futurist movement which partially inspired the Fascist movement also held considerable sway, but the prominence of Futurist architecture was largely overshadowed by the influence of Roman forms.